http://iet.metastore.ingenta.com
1887

access icon free Optimal and accurate design of fractional-order digital differentiator – an evolutionary approach

Loading full text...

Full text loading...

/deliver/fulltext/iet-spr/11/2/IET-SPR.2016.0201.html;jsessionid=16tykt5tyxggf.x-iet-live-01?itemId=%2fcontent%2fjournals%2f10.1049%2fiet-spr.2016.0201&mimeType=html&fmt=ahah

References

    1. 1)
      • 1. Oldham, K.B., Spanier, J.: ‘The fractional calculus’ (Academic Press, New York, 1974).
    2. 2)
      • 2. West, B.J., Bologna, M., Grigolini, P.: ‘Physics of fractal operators’ (Springer Verlag, New York, 2003).
    3. 3)
      • 3. Engheta, N.: ‘On fractional calculus and fractional multipoles in electromagnetism’, IEEE Trans. Antennas Propag., 1996, 44, (4), pp. 554566.
    4. 4)
      • 4. Podlubny, I.: ‘Fractional-order systems and PIλDμ –controllers’, IEEE Trans. Autom. Control, 1999, 44, (1), pp. 208214.
    5. 5)
      • 5. Oustaloup, A., Levron, F., Mathieu, B., et al: ‘Frequency-band complex noninteger differentiator: characterization and synthesis’, IEEE Trans. Circuits Syst. I, 2000, 47, (1), pp. 2539.
    6. 6)
      • 6. Mathieu, B., Melchior, P., Oustaloup, A., et al: ‘Fractional differentiation for edge detection’, Signal Process., 2003, 83, (3), pp. 24212432.
    7. 7)
      • 7. Benmalek, M., Charef, A.: ‘Digital fractional order operators for R-wave detection in electrocardiogram signal’, IET Signal Process., 2009, 3, (5), pp. 381391.
    8. 8)
      • 8. Galvão, R.K.H., Hadjiloucas, S., Kienitz, K.H., et al: ‘Fractional order modeling of large three-dimensional RC networks’, IEEE Trans. Circuits Syst. I, Regul. Pap., 2013, 60, (3), pp. 624637.
    9. 9)
      • 9. Chen, Y.Q., Vinagre, B.M.: ‘A new IIR-type digital fractional order differentiator’, Signal Process., 2003, 83, (11), pp. 23592365.
    10. 10)
      • 10. Chen, Y.Q., Moore, K.L.: ‘Discretization schemes for fractional-order differentiators and integrators’, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 2002, 49, (3), pp. 363367.
    11. 11)
      • 11. Vinagre, B.M., Chen, Y.Q., Petras, I.: ‘Two direct Tustin discretization methods for fractional-order differentiator/integrator’, J. Franklin Inst., 2003, 340, (5), pp. 349362.
    12. 12)
      • 12. Maione, G.: ‘A rational discrete approximation to the operator s0.5’, IEEE Signal Process. Lett., 2005, 13, (3), pp. 141144.
    13. 13)
      • 13. Barbosa, R.S., Machado, J.A.T., Silva, M.F.: ‘Time domain design of fractional differ integrators using least-squares’, Signal Process., 2006, 86, (10), pp. 25672581.
    14. 14)
      • 14. Ferdi, Y.: ‘Computation of fractional order derivative and integral via power series expansion and signal modeling’, Nonlinear Dyn., 2006, 46, (1–2), pp. 115.
    15. 15)
      • 15. Tseng, C.C.: ‘Improved design of digital fractional order differentiators using fractional sample delay’, IEEE Trans. Circuits Syst. I, Regul. Pap., 2006, 53, (1), pp. 193203.
    16. 16)
      • 16. Tseng, C.C., Lee, S.L.: ‘Design of fractional order digital differentiator using radial basis function’, IEEE Trans. Circuits Syst. I, Regul. Pap., 2010, 57, (7), pp. 17081718.
    17. 17)
      • 17. Gupta, M., Varshney, P., Visweswaran, G.S.: ‘Digital fractional-order differentiator and integrator models based on first-order and higher order operators’, Int. J. Circuit Theory Appl., 2011, 39, (5), pp. 461474.
    18. 18)
      • 18. Romero, M., de Madrid, A.P., Manoso, C., et al: ‘IIR approximations to the fractional differentiator/integrator using Chebyshev polynomials theory’, ISA Trans., 2013, 52, (4), pp. 461468.
    19. 19)
      • 19. Maione, G.: ‘Closed-form rational approximations of fractional, analog and digital differentiators/integrators’, IEEE J. Emerg. Sel. Top. Circuits Syst., 2013, 3, (3), pp. 322329.
    20. 20)
      • 20. Rana, K.P.S., Kumar, V., Garg, Y., et al: ‘Efficient design of discrete fractional order differentiators using Nelder-Mead simplex algorithm’, Circuits Syst. Signal Process., 2016, 35, (6), pp. 21552188.
    21. 21)
      • 21. Gupta, M., Yadav, R.: ‘New improved fractional order differentiator models based on optimized digital differentiators’, Sci. World J., 2014, 2014, pp. 111, article id – 741395.
    22. 22)
      • 22. Yadav, R., Gupta, M.: ‘Approximations of higher-order fractional differentiators and integrators using indirect discretization’, Turk. J. Electr. Eng. Comput. Sci., 2015, 23, pp. 666680.
    23. 23)
      • 23. Leulmi, F., Ferdi, Y.: ‘Improved digital rational approximation of the operator sα using second-order s-to-z transform and signal modeling’, Circuits Syst. Signal Process., 2015, 34, (6), pp. 18691891.
    24. 24)
      • 24. Karaboga, N.: ‘A new design method based on artificial bee colony algorithm for digital IIR filters’, J. Franklin Inst., 2009, 346, (4), pp. 328348.
    25. 25)
      • 25. Mirjalili, S., Lewis, A.: ‘Adaptive gbest-guided gravitational search algorithm’, Neural Comput. Appl., 2014, 25, (7), pp. 15691584.
    26. 26)
      • 26. Saha, S.K., Kar, R., Mandal, D., et al: ‘Seeker optimization algorithm: application to the design of linear phase finite impulse response filter’, IET Signal Process., 2012, 6, (8), pp. 763771.
    27. 27)
      • 27. Saha, S.K., Ghoshal, S.P., Kar, R., et al: ‘Cat swarm optimization algorithm for optimal linear phase FIR filter design’, ISA Trans., 2013, 52, (6), pp. 781794.
    28. 28)
      • 28. Goldberg, D.B.: ‘Genetic algorithms in search optimization and machine learning’ (Addison-Wesley, San Francisco, 1989).
    29. 29)
      • 29. Kennedy, J., Eberhart, R.: ‘Particle swarm optimization’. Proc. IEEE Int. Conf. Neural Networks, Perth, Australia, 1995, vol. 4, pp. 19421948.
    30. 30)
      • 30. Storn, R., Price, K.: ‘Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces’, J. Glob. Optim., 1997, 11, (4), pp. 341359.
    31. 31)
      • 31. Ababneh, J.I., Bataineh, M.H.: ‘Linear phase FIR filter design using particle swarm optimization and genetic algorithms’, Digital Signal Process., 2008, 18, (4), pp. 657668.
    32. 32)
      • 32. Karaboga, N., Cetinkayal, B.: ‘Design of digital FIR filters using differential evolution algorithm’, Circuits Syst. Signal Process., 2006, 25, (5), pp. 649660.
    33. 33)
      • 33. Rashedi, E., Nezamabadi-Pour, H., Saryazdi, S.: ‘GSA: a gravitational search algorithm’, Inf. Sci., 2009, 179, (13), pp. 22322248.
    34. 34)
      • 34. Montgomery, D.C., Runger, G.C.: ‘Applied statistics and probability for engineers’ (John Wiley and Sons, Inc., 2003, 3rd edn.).
    35. 35)
      • 35. Abramowitz, M., Stegun, I.A.: ‘Handbook of mathematical functions’ (Dover Publications, New York, 1974).
    36. 36)
      • 36. Feliu, V., Rattan, K.S., Brown, H.B.: ‘Adaptive control of a single-link flexible manipulator’, IEEE Control Syst. Mag., 1990, 10, (2), pp. 2933.
    37. 37)
      • 37. Rao, V.G., Bernstein, D.S.: ‘Naïve control of the double integrator’, IEEE Control Syst. Mag., 2001, 21, (5), pp. 8697.
    38. 38)
      • 38. Debnath, L.: ‘Integral transforms and their applications’ (CRC Press, Boca Raton, FL, 1995).
    39. 39)
      • 39. Podlubny, I.: ‘Fractional differential equations’ (Academic Press, San Diego, 1999).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-spr.2016.0201
Loading

Related content

content/journals/10.1049/iet-spr.2016.0201
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address